Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
from(X) |
→ cons(X,n__from(s(X))) |
| 2: |
|
after(0,XS) |
→ XS |
| 3: |
|
after(s(N),cons(X,XS)) |
→ after(N,activate(XS)) |
| 4: |
|
from(X) |
→ n__from(X) |
| 5: |
|
activate(n__from(X)) |
→ from(X) |
| 6: |
|
activate(X) |
→ X |
|
There are 3 dependency pairs:
|
| 7: |
|
AFTER(s(N),cons(X,XS)) |
→ AFTER(N,activate(XS)) |
| 8: |
|
AFTER(s(N),cons(X,XS)) |
→ ACTIVATE(XS) |
| 9: |
|
ACTIVATE(n__from(X)) |
→ FROM(X) |
|
The approximated dependency graph contains one SCC:
{7}.
-
Consider the SCC {7}.
The usable rules are {1,4-6}.
By taking the AF π with
π(activate) = π(AFTER) = π(cons) = π(from) = π(n__from) = 1 together with
the lexicographic path order with
empty precedence,
the rules in {1,4-6}
are weakly decreasing and
rule 7
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.04 seconds)
--- May 3, 2006